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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{9}{4}}}{w^{\frac{11}{4}}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{9}{4}}}{w^{\frac{11}{4}}}

\newline

Write your answer in the form

A

or

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Apply Exponent Rule: We have the expression: $\newline$ $w^{\frac{9}{4}} / w^{\frac{11}{4}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Divide Exponents: Apply the rule for dividing exponents: $\newline$ $w^{\frac{9}{4}} / w^{\frac{11}{4}}$ $\newline$ = $w^{\frac{9}{4} - \frac{11}{4}}$ $\newline$ = $w^{-\frac{2}{4}}$
Simplify Negative Exponent: Simplify the negative exponent: $w^{(-2/4)}$ Since we want all exponents to be positive, we can rewrite this as: $w^{(-2/4)} = \frac{1}{w^{(2/4)}}$
Simplify Fraction in Exponent: Simplify the fraction in the exponent: $\newline$ $\frac{1}{w^{\frac{2}{4}}}$ $\newline$ Since $\frac{2}{4}$ simplifies to $\frac{1}{2}$ , we have: $\newline$ $\frac{1}{w^{\frac{1}{2}}}$

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